This paper employs fuzzy variables instead of deterministic variables for job times in a project network. A fuzzy variable has its value restricted by a possibility distribution. This paper utilizes the triangular possibility distribution which has three estimated times. That is normal, resonable, and crash job times. This paper develops a fuzzy k-longest path algorithm, by utilizing the k-longest path algorithm. This algorithm will be useful to control the project the project network by considering the project completion possibility.